A numerical issue in calculating the coupled carbon and water fluxes in a climate model

Abstract

The Community Land Model (CLM) uses a fixed‐point iteration approach to solve the coupled photosynthesis and stomatal conductance model (A– gs). Here we demonstrate that this approach does not converge in its iterative calculation of gross primary production (GPP) and transpiration in large portions of land surface, because the coupled A– gsmodel does not always comply with a condition (the fixed‐point theorem) required by the fixed‐point approach for convergence. This iteration fails more frequently in some regions of the world than in others, leading to regionally varying uncertainty and global biases in the estimated carbon and water fluxes. Moreover, CLM applies an artificial constraint to the water vapor pressure of canopy air in its calculations ofA– gs, with an intention to prevent the ‘numerical instability’ arising from the fixed‐point approach. Our results show that this constraint reduces but does not prevent the occurrence of nonconvergence. Since this constraint is artificial, it can bias GPP and transpiration simulations. We then propose a Newton‐Raphson iteration scheme to replace the fixed‐point approach and show that this new approach can ensure convergence, does not require an artificial constraint on the atmospheric water vapor pressure, and is computationally efficient. On the other hand, the default fixed‐point treatment in CLM leads to a ∼2.7 PgCyr−1overestimation of GPP globally but with much higher regional biases (∼27%). We suggest that the current fixed‐point treatment in CLM be replaced with the Newton‐Raphson approach and that the artificial constraint on the atmospheric water vapor pressure be removed.